Vapnik-Chervonenkis density in some theories without the independence property, I

DOI10.1090/tran/6659zbMath1423.03119arXiv1109.5438OpenAlexW1975177932WikidataQ59892890 ScholiaQ59892890MaRDI QIDQ2790718

Dugald Macpherson, Alf Dolich, Matthias Aschenbrenner, Deirdre Haskell, Sergei Starchenko

Publication date: 8 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.5438

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Model theory of ordered structures; o-minimality (03C64)

Related Items (27)

Structure and regularity for subsets of groups with finite VC-dimension ⋮ Vapnik-Chervonenkis dimension and density on Johnson and Hamming graphs ⋮ Unavoidable subprojections in union-closed set systems of infinite breadth ⋮ On VC-minimal theories and variants ⋮ Computability of validity and satisfiability in probability logics over finite and countable models ⋮ Combinatorial properties of nonarchimedean convex sets ⋮ Burden in Henselian valued fields ⋮ Neighbourhood complexity of graphs of bounded twin-width ⋮ A family of dp-minimal expansions of \((\mathbb{Z}; +)\) ⋮ A definable \((p,q)\)-theorem for NIP theories ⋮ The classification of dp-minimal and dp-small fields ⋮ Profinite groups with NIP theory andp-adic analytic groups ⋮ RAMSEY GROWTH IN SOME NIP STRUCTURES ⋮ THERE ARE NO INTERMEDIATE STRUCTURES BETWEEN THE GROUP OF INTEGERS AND PRESBURGER ARITHMETIC ⋮ On some dynamical aspects of NIP theories ⋮ Definability of types and VC density in differential topological fields ⋮ DP-MINIMAL VALUED FIELDS ⋮ THE DP-RANK OF ABELIAN GROUPS ⋮ A NEW DP-MINIMAL EXPANSION OF THE INTEGERS ⋮ Cutting lemma and Zarankiewicz's problem in distal structures ⋮ VC-density for trees ⋮ On \(n\)-dependence ⋮ On VC-density in VC-minimal theories ⋮ THICKET DENSITY ⋮ Externally definable sets and dependent pairs II ⋮ Additivity of the dp-rank ⋮ Model Theory in Algebra, Analysis and Arithmetic: A Preface

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